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Three logicians, Carroll, Kurt and Kleene, are captured by the evil villainous mastermind, Moriarty. They are put in adjacent cells each of which contains a number of coins. All of them can count the number of coins in their own cells, but not in anyone else’s. They are told that each cell has at least one coin, and at most nine coins, and no two cells have the same number of coins. The logicians must use their skills of deductive reasoning to escape their cells. The three of them will ask Moriarty a single (yes or no) question each, which he will answer truthfully ‘Yes’ or ‘No’. Every one hears the questions and the answers. Moriarty will free the logicians only if one of them correctly works out the total number of coins in all three cells. Here’s how the conversation between them ensues.
Carroll: Is the total number of coins an even number?
Moriarty: No.
Kurt: Is the total number of coins a prime number?
Moriarty: No.
If Kleene has ﬁve coins in his cell, what question should he ask Moriarty in order to ensure that at least one of the logicians work out the total number of coins in the cells?